C 2 99 ] 
Forces of the Column C N. Now to endue our Sphe- 
roids with this Property, we will refume the Expreffion 
of the centrifugal Force in E, which we found Art. 
XIV. which will give ^ 
Scf e 
*4-P, 
4 
Scge 
i + P 
■) 
3+-P x 5 + P 3 4<l K 5 + q 
for that Part of the centrifugal Force which afts ac- 
cording to CM, in any Place M, by expunging the 
Terms in which a, a. would be found. This Value 
being multiply ’d by r, and by the Dcnfity, will give 
('when we have taken the Fluent) - _ — — — 
2 +P X ^+P X 5 +;P 
+ 8cf g e 2+p 4q^ 8cfge 2 + P + qx 
2 +P' x 3 + q x 5+4 2 + qX3+pX5 + p 
-p g -iL- -~L for the Silm of the centri- 
2 +q x 3 +q>< 5 +q 
fugal Forces of the Column CN> (till expunging thofe 
Terms in which either a a or. a A are found. 
Then making this* Expreifion equal to 
2 + P + q A 
4 2 p c P* e 2 ^ 2 P a | 8 -f- 4 . t> c f v e 
I +P x 3+P x 5+P 2+p+q x 3 4-pX5‘ i f-p 
8 -f- 4. q c f g e 2 “^~ P 4-^-2 qcg s e 2 ^" 2 C * 
A. 
— ? 
2 +p+q x 3+q x 5+.q ' i+q x 3+q x 5+q 
which is the Difference of the Weight of the Co- 
lumn at. the Pole C B, from the Sumuof the Attrafti- 
ons of the Column CN, we fhall have the Equation 
ppff a p q f g 
’74^X^+pxH- : P x 5+P ‘ a + P + q x 3 + P x 5+P x 2 + q 
} 2pqfg ^ q q g g 
^i-fp 4 -qxT+qX 5 + q x 2 +P i-f qXa+qX 3 -(-q x 5 + q 
where we have put e=i, for the greater Simplicity of 
Calculation. 
XXXII, 
■ 3 = 0 , 
